Composite Repair

Composite Repair (structures/composites/composite-repair)

Use when you must size a bonded scarf repair for a damaged composite laminate: computing the scarf length from the parent thickness and the scarf angle, the average adhesive shear stress carried by the scarf joint when the parent laminate runs at its applied stress, the required scarf angle for an adhesive shear allowable, and the external patch thickness that restores the parent in-plane stiffness. This leaf implements the standard uniform-stress scarf joint model in pure Python, stdlib only, with no material constants so it applies to any carbon/epoxy or glass/epoxy system. It pairs with the other composites leaves: laminate-stiffness and failure-criteria provide the parent layup modulus and the applied laminate stress used as inputs here, and cmh17-allowables frames the adhesive and laminate allowables.

Domain quick reference

• Scarf length for a full-depth scarf: L = thickness / tan(theta), where theta is the scarf angle measured from the laminate plane. A shallower angle gives a longer scarf.
• Average adhesive shear stress (uniform-stress scarf model): tau = sigma * sin(theta) * cos(theta), equivalently tau = (sigma / 2) * sin(2 * theta), with sigma the far-field parent laminate stress carried across the scarf plane.
• Required scarf angle for an adhesive shear allowable tau_a: theta_req = 0.5 * asin(2 * tau_a / sigma). When 2 * tau_a / sigma exceeds 1.0 no real scarf angle can carry the load at that stress; the repair cannot be made in scarf.
• Stiffness-matched external patch: t_patch = t_parent * E_parent / E_patch, matching the parent in-plane stiffness when the patch runs at the parent strain.
• Margin: margin = tau_a / tau - 1. A negative margin means the chosen scarf angle does not clear the allowable, and the scarf must be made shallower (longer) so the adhesive shear drops to the allowable.
• Angles are degrees for callers; repair_sizing takes SI inputs (m, Pa) and returns scarf_length_m, adhesive_shear_Pa and patch_thickness_m.
• CMH-17 frames bonded repair practice for composite structures; the relations above are standard engineering methodology, summary-only.

Workflow

1. Fix the repair inputs: parent laminate thickness, the applied laminate stress at the repair location, the parent modulus, the patch material modulus, a chosen scarf angle, and the adhesive shear allowable.
2. Compute the scarf length with scarf_length from the parent thickness and the chosen scarf angle.
3. Compute the average adhesive shear stress with adhesive_shear_stress from the parent stress and the chosen scarf angle.
4. Check the scarf angle against the allowable with required_scarf_angle: if the required angle differs from the chosen angle in the steep direction, the chosen scarf does not clear the allowable.
5. Size the external patch with patch_thickness_for_stiffness from the parent thickness and the two moduli; a stiffer patch is thinner, a softer patch is thicker.
6. Run repair_sizing for the full summary including the margin, and re-scarf at the required angle whenever the margin is negative.
7. Confirm the deterministic checks with the contract test scripts/test_composite_repair.py.

Worked example

Carbon/epoxy parent: thickness 3.0 mm, applied laminate stress 300 MPa, parent modulus 70 GPa, patch material modulus 70 GPa (same material), scarf angle 3 degrees, adhesive shear allowable 12 MPa.

• Scarf length: L = 3.0 / tan(3 deg) = 57.24 mm (scarf_length(3.0, 3.0) = 57.24 mm, within the 50-65 mm band).
• Adhesive shear stress: tau = 300 * sin(3 deg) * cos(3 deg) = 15.68 MPa (adhesive_shear_stress(300.0, 3.0) = 15.679 MPa, within the 14-17 MPa band).
• Required scarf angle for the 12 MPa allowable: theta_req = 0.5 * asin(24 / 300) = 2.29 deg (required_scarf_angle gives 2.294 deg, within the 2.0-2.6 deg band).
• Patch thickness: t_patch = 3.0 * 70 / 70 = 3.0 mm exactly, the same-material identity.
• Margin at 3 degrees: 12 / 15.68 - 1 = -0.235. The chosen 3 deg scarf FAILS the 12 MPa allowable; the repair must be re-scarfed shallower.
• Passing check at 2.2 degrees: tau = 300 * sin(2.2 deg) * cos(2.2 deg) = 11.51 MPa, margin = 12 / 11.51 - 1 = +0.043, so a 2.2 deg scarf clears the allowable.

Pitfalls

• Sizing the scarf at a steep angle out of habit: a shallower angle gives a longer scarf and a lower adhesive shear; the 3 deg scarf in the worked example fails the 12 MPa allowable (margin -0.235) and the repair must be re-scarfed to about 2.29 deg.
• Demanding a scarf when no scarf can work: when 2 * tau_a / sigma exceeds 1.0 no real scarf angle carries the load and the functions raise ValueError - the repair cannot be made in scarf at that stress.
• Checking the margin against the chosen angle only: the margin is tau_a / tau - 1 at the CHOSEN angle; a negative margin means re-scarf shallower, and the required-angle round trip (scarfing at the required angle reproduces the allowable) is the design check.
• Forgetting the modulus match on the patch: the external patch is sized for stiffness t_patch = t_parent * E_parent / E_patch, so a stiffer patch is thinner and a softer patch is thicker; the same-material identity t_patch = t holds exactly.
• Using degrees where the model wants radians: the public angle helpers take degrees while repair_sizing takes SI inputs and returns SI outputs - mixing the two conventions silently skews the scarf length and shear.
• Confusing the repair model with a lap joint: this leaf is the uniform-stress scarf model; lap joint analysis belongs to adhesive-bonded-joints, and mechanically fastened repairs to composite-bolted-joints.

Verification

• Confirm scarf_length(3.0, 3.0) returns 57.24 mm and sits in 50-65 mm.
• Confirm adhesive_shear_stress(300.0, 3.0) returns 15.679 MPa and sits in 14-17 MPa.
• Confirm required_scarf_angle(300.0, 12.0) returns 2.294 deg and sits in 2.0-2.6 deg.
• Confirm the margin is negative for the 3 deg case (-0.235) and positive for the 2.2 deg case (+0.043).
• Confirm the patch identity patch_thickness_for_stiffness(t, E, E) == t and the sin-cos form of the shear equals the (sigma / 2) * sin(2 theta) form.
• Confirm every non-positive thickness, stress, modulus or allowable, every angle at or beyond 90 degrees, and every required_scarf_angle call with 2 * tau_a / sigma > 1 (for example sigma = 100 MPa, tau_a = 80 MPa) raises ValueError.
• Run the contract test offline: python3 scripts/test_composite_repair.py (34 tests, deterministic).

Related leaves

• structures/composites/adhesive-bonded-joints: lap joint bonded analysis in the same pack; lap geometry analysis is not part of this leaf.
• structures/composites/composite-bolted-joints: mechanically fastened patch attachment analysis, the alternative to a bonded repair.
• structures/composites/laminate-stiffness: parent layup stiffness, an input to the stiffness-matched patch sizing here.
• structures/composites/cmh17-allowables: laminate and adhesive allowables used as inputs here.
• structures/composites/delamination-growth: fracture assessment of interlaminar damage growth in the parent around the repair location.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_composite_repair.py

The test covers the worked example contract (scarf length 57.24 mm, adhesive shear 15.68 MPa, required angle 2.29 deg, patch identity 3.0 mm), the magnitude bounds from the spec (50-65 mm, 14-17 MPa, 2.0-2.6 deg), the margin signs for both the failing 3 deg case and the passing 2.2 deg case, the sin-cos closed-form identity, the required-angle round-trip (scarfing at the required angle reproduces the allowable), determinism, and ValueError rejection of non-physical inputs.

Compliance

• Standards referenced, not reproduced: CMH-17 (the Composite Materials Handbook) is referenced for bonded scarf repair practice; the repair sizing relations above are standard engineering methodology, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.